The optimal control problem with that system was investigated in [1]}. Therein, the adjoint equations for the functional \(\phi (x(t_f))\)  were established, herein parts of these equations are presented to expose jumps in adjoint variables.
\({\rm for}\ k = N-1,\ldots ,k_{t}+1& \nonumber \\\Lambda ^2(k)&=- F^2_X(k_t)^T\left[F^2_{X^+}(k_t)\right]^{-T}\Lambda ^2(k+1)\\\Lambda ^{2+}(k_t)&=- F^2_X(k_t)^T\left[F^2_{X^+}(k_t)\right]^{-T}\Lambda ^2(k_t+1)\\\tilde{\Lambda }^{1-}(k_t)+\pi (k_t) \left( g_x(k_t) \right)^T &=\tilde{\Lambda }^{2+}(k_t) \\\Lambda ^{1-}(k_t)^T \left[ F^1_{X^+}(k_t-1)\right]^{-1}F^1_h(k_t-1) & = \Lambda ^2(k_t+1)^T\left[F^2_{X^+}(k_t)\right]^{-1}F^2_h(k_t),\\\Lambda ^1(k_t-1)&=- F^1_X(k_t)^T\left[F^1_{X^+}(k_t)\right]^{-T}\Lambda ^{1-}(k_t)\\{\rm for}\ k = k_t-2,\ldots ,1 \nonumber \\\Lambda ^1(k)&=- F^1_X(k_t)^T\left[F^1_{X^+}(k_t)\right]^{-T}\Lambda ^1(k+1).\) 
